Article ID: CBB001024148

Abduction, Tomography, and Other Inverse Problems (2011)

unapi

Charles S. Peirce introduced in the late 19th century the notion of abduction as inference from effects to causes, or from observational data to explanatory theories. Abductive reasoning has become a major theme in contemporary logic, philosophy of science, and artificial intelligence. This paper argues that the new growing branch of applied mathematics called inverse problems deals successfully with various kinds of abductive inference within a variety of scientific disciplines. The fundamental theorem about the inverse reconstruction of plane functions from their line integrals was proved by Johann Radon already in 1917. The practical applications of Radon's theorem and its generalizations include computerized tomography which became a routine imaging technique of diagnostic medicine in the 1970s.

...More
Citation URI
https://data.isiscb.org/isis/citation/CBB001024148/

Similar Citations

Article Campos, Daniel G.; (2011)
On the Distinction between Peirce's Abduction and Lipton's Inference to the Best Explanation (/isis/citation/CBB001211461/)

Article Michael J. Flexer; (2020)
If p0, Then 1: The Impossibility of Thinking Out Cases (/isis/citation/CBB601183479/)

Article Daude, Olivier; (2011)
Le pragmaticisme et la question du témoignage (/isis/citation/CBB001024474/)

Book Shin, Sun-Joo; (2002)
The Iconic Logic of Peirce's Graphs (/isis/citation/CBB000500174/)

Book Brady, Geraldine; (2000)
From Peirce to Skolem: A Neglected Chapter in the History of Logic (/isis/citation/CBB000102342/)

Book Ekeland, Ivar; (2006)
The Best of All Possible Worlds: Mathematics and Destiny (/isis/citation/CBB000741783/)

Book Patterson, Douglas; (2008)
New Essays on Tarski and Philosophy (/isis/citation/CBB001232382/)

Book Tieszen, Richard L.; (2011)
After Gödel: Platonism and Rationalism in Mathematics and Logic (/isis/citation/CBB001210605/)

Book Shanker, Stuart; (2003)
Philosophy of Science, Logic and Mathematics in the 20th Century (/isis/citation/CBB000502126/)

Book Bernays, Paul; (2003)
Philosophie des mathématiques (/isis/citation/CBB000501923/)

Book Heijenoort, Jean van; (2002)
From Frege to Gödel: A Source Book in Mathematical Logic, 1879-1931 (/isis/citation/CBB000201415/)

Chapter Weiner, Joan; (2010)
Understanding Frege's Project (/isis/citation/CBB001211648/)

Article Franks, Curtis; (2009)
The Gödelian Inferences (/isis/citation/CBB001211043/)

Article de Rouilhan, Philippe; (2012)
In Defense of Logical Universalism: Taking Issue with Jean van Heijenoort (/isis/citation/CBB001214124/)

Book George, Alexander; Velleman, Daniel J.; (2002)
Philosophies of Mathematics (/isis/citation/CBB000201738/)

Article Manzano, Maria; Alonso, Enrique; (2014)
Completeness: From Gödel to Henkin (/isis/citation/CBB001213927/)

Essay Review Klement, Kevin C.; (2007--2008)
A New Century in the Life of a Paradox (/isis/citation/CBB001567033/)

Article Plutynski, Anya; (2011)
Four Problems of Abduction: A Brief History (/isis/citation/CBB001230106/)

Authors & Contributors
Flexer, Michael J.
Weiner, Joan
Velleman, Daniel J.
Tieszen, Richard L.
Shin, Sun-Joo
Shanker, Stuart G.
Concepts
Logic
Philosophy of mathematics
Mathematics
Philosophy
Abduction
Philosophy of science
Time Periods
20th century
19th century
21st century
20th century, early
18th century
Places
United States
Poland
Massachusetts (U.S.)
Comments

Be the first to comment!

{{ comment.created_by.username }} on {{ comment.created_on | date:'medium' }}

Log in or register to comment